Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented

In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)

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Inverse and Ill-posed Problems: Theory and Applications

The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included

Determination of the impedance of a multiperforated plate: an inverse problem

International audienceIn the context of time-harmonic wave equation, we solve the inverse problem to find an impedance coefficient thanks to measurement of the velocity